Using Wave Propagation Simulations and Convolutional Neural Networks to Retrieve Thin Film Thickness from Hyperspectral Images

Ill-posed inversion problems are one of the major challenges when there is a need to combine measurements with the theory and numerical model. In this study, we demonstrate the use of wave propagation simulations to train a convolutional neural network (CNN) for retrieving sub-wavelength thickness profiles of thin film coatings from hyperspectral images. The simulations are produced by solving numerically one-dimensional wave equation with a method based on Discrete Exterior Calculus (DEC). This approach provides a powerful tool to produce large sets of training data for the neural network. CNN was verified by simulated verification sets and measured reflectance spectra, both of which showed strong correlations. A hyperspectral image that cover a region of sample provides sufficient number of spectra for reliable thickness analysis, but at the same time allows the use of a small detection spots to solve non-uniformity problems. The non-uniformity of film thickness is characterized and the results are promising. The approach introduced in this study provides a potential solution to the challenges of thin film analytics in the field of sub-wavelength thickness and its non-uniformity.